1. 4.7 The Quadratic Formula Learning goals
solve quadratic equations using the Quadratic Formula
determine the number of solutions by using the discriminant

2. If a quadratic equation is written in standard form
then it can be solved with the Quadratic Formula

3. Ex 1 Solve using the QF

4. Ex 2 Solve using the QF

5. discriminant : value beneath the radical
Value of Discriminant
Number of Solutions
Type of Solutions
Graph Intercepts
Graph
> 0
and a perfect square 2
rational
2 x-intercepts
and NOT a perfect square
irrational
= 0  1
1 x-intercept
< 0
complex; no real
no x-intercepts

6. Ex 3 Determine the type & number of solutions.

7. Ex 4
A player throws a ball up and toward a wall that is 17 feet high. The height h in feet of the ball t seconds after it leaves the player’s hand is modeled by the equation above. If the ball makes it to wall, will it go over the wall or hit the wall?

8. Ex 5
Your school’s jazz band is selling CDs as a fund raiser. The total profit p depends on the amount charged for each CD. The equation above models the profit of the fund raiser. What is the least amount, in dollars, you can charge for a CD to make a profit of $200?